Measurement & Geometry 3.6 : Measurement & Geometry 3.6 Here is the exact Content Standard for 4th grade:
3.6 Visualize, describe, and make models of geometric solids (e.g., prisms, pyramids) in terms of the number and shape of faces, edges, and vertices; interpret two-dimensional representations of three-dimensional objects; and draw patterns (of faces) for a solid that, when cut and folded, will make a model of the solid. Wow! That’s a lot of words! The good news is that you already know many of these concepts. “Three dimensional” is an adjective that describes the real world that you live in, where objects have length, width, depth (or height) – in other words, 3 dimensions! If you’ve ever played a modern video game, you’ve already experienced a 2-dimensional representation of your 3-dimensional world. 3D means “3-dimensional”
Let’s refresh your understanding of 2-dimensional concepts: : Let’s refresh your understanding of 2-dimensional concepts: For most of this year you’ve been learning about 2-dimensional concepts. For example, graphing has been 2-dimensional because you used only an X axis and a Y axis to show the two dimensions. You’ll understand 3-dimensional geometry faster if you first understand that 3-dimensional graphs, figures and representations contain another axis called the Z axis, which adds the third dimension. You also learned that AREA is a measure consisting of two dimensions: LENGTH & WIDTH.
2-Dimensional representations of 3-D Objects : 2-Dimensional representations of 3-D Objects A real 3-dimensional solid, such as an Egyptian pyramid, can be represented by a 2-dimensional drawing, such as the red lines that have been added to this photo. Remember: Even if the drawing contains different colors to make the object seem more “real,” it is still just a 2-dimensional representation of a 3-dimensional object. Vocabulary: “representation” is a fancy word that means “drawing.”
2-Dimensional representations of 3-D Objects : 2-Dimensional representations of 3-D Objects “…faces, edges, and vertices” (Measurement & Geometry 3.6) You’ve already learned that a 2-dimensional angle has one vertex, and that a 2-dimensional triangle has 3 vertices. A 2-dimensional representation of a 3-D object will show the object’s vertices, edges, and faces. edge: a line segment where 2 faces meet. vertex: a point where 3 or more edges meet. face: a “side” of the object. So how do you draw a
Geometric Solids : Geometric Solids Here are various geometric solids that you should recognize by name. You should also be able to count the number of vertices, edges, and faces. Rectangular prism: shaped like a shoe box!
8 vertices, 6 faces, 12 edges Square pyramid: the bottom face is a square
5 vertices, 5 faces, 8 edges Rectangular pyramid: the bottom face is a rectangle
Other details match the square pyramid. Cube: each of the 6 faces is a square
Other details match the rectangular prism
Geometric Patterns or “Nets” : Geometric Patterns or “Nets” Have you ever seen a 2-dimensonal pattern that a dressmaker uses to create a 3-dimensional dress? A 3-dimensional geometric shape also has a 2-dimensional pattern (sometimes called a net) that you can cut out and fold together to create the 3-D object. cube